**NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.5 – Practical Geometry**

**NCERT Solutions for Class 8 Maths ****Chapter 4 Exercise 4.5 – Practical Geometry****, has been designed by the NCERT to test the knowledge of the student on the topic – Constructing a Quadrilateral – When other special properties are known.**

**Draw the following.**

**1. The square READ with RE = 5.1 cm.**

**Solution:**

RE = EA = AD = DR = 5.1 cm (All sides of a square are equal)

∠R = ∠E = ∠A = ∠D = 90° (All angles of a square are equal)

**Steps of construction**

- Step 1. Draw the side RE = 5.1 cm
- Step 2. Draw ∠REA = 90°, such that EA = 5.1 cm
- Step 3. Draw ∠ERD = 90°, such that RD = 5.1 cm
- Step 4. Joint the points D and A

READ is the required square.

**2. A rhombus whose diagonals are 5.2 cm and 6.4 cm long.**

**Solution:**

**Steps of construction**

- Step 1. Draw the side AC = 5.2 cm
- Step 2. Draw the perpendicular bisector of AC, intersecting it at O
- Step 3. With O as centre and 3.2 cm (= 6.4/2) as radius, draw arcs intersecting the perpendicular bisector at B and D
- Step 4. Joint the points AB, BC, CD and DA

ABCD is the required rhombus.

**3. A rectangle with adjacent sides of lengths 5 cm and 4 cm.**

**Solution:**

**Steps of construction**

- Step 1. Draw the side AB = 5 cm
- Step 2. Draw ∠ABC = 90°, such that BC = 4 cm
- Step 3. Draw ∠BAD = 90°, such that AD = 4 cm
- Step 4. Joint the points C and D

ABCD is the required rectangle.

**4. A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?**

**Solution:**

Let ∠O = θ (θ may vary)

OK = AY = 5.5 cm (Opposite sides of a parallelogram are equal)

KA = YO = 4.2 cm

**Steps of construction**

- Step 1. Draw the side OK = 5.5 cm
- Step 2. Draw ∠KOY = θ°, such that OY = 4.2 cm
- Step 3. With K as centre and radius 4.2 cm (= KA), draw an arc
- Step 4. With Y as centre and radius 5.5 cm (= AY), draw an arc intersecting the previous arc at point A
- Step 5. Join AK and AY

OKAY is the required parallelogram.

Since, θ can vary

Therefore, parallelogram OKAY is not unique.

**The next Exercise for** **NCERT Solutions for Class 8 Maths Chapter 5 Exercise 5.1 – Data Handling can be accessed by clicking here**

** Maths – NCERT Solutions Class 8**

**NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.5 – Practical Geometry**

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